Microwave signatures of ${\mathbb{Z}}_2$ and ${\mathbb{Z}}_4$ fractional Josephson effects

Abstract

We present a many-body exact diagonalization study of the ${\mathbb{Z}}_2$ and ${\mathbb{Z}}_4$ Josephson effects in circuit quantum electrodynamics architectures. Numerical simulations are conducted on Kitaev chain Josephson junctions hosting nearest-neighbor Coulomb interactions. The low-energy effective theory of highly transparent Kitaev chain junctions is shown to be identical to that of junctions created at the edge of a quantum spin-Hall insulator. By capacitively coupling the interacting junction to a microwave resonator, we predict signatures of the fractional Josephson effects on the cavity frequency and on time-resolved reflectivity measurements.

arXiv comment16 pages, 11 figures

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• Theory of topological spin Josephson junctions
• Topological Josephson Bifurcation Amplifier: Semiclassical theory